Normal distribution worksheet with answers

Free printable Normal distribution worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
μ = 500454P = ?

The battery lifetimes are normally distributed with mean 500 h and standard deviation 40 h. What fraction is above 454 h? Find P(X > x) as a decimal.

μ = 500σ = 40x = 454
P(X > x) =
2.Easy
−3−2−10123zshaded area to the left of z = 0.9177

Drag z so that the shaded area under the standard normal curve, to the left of z, is 0.9177. Find z to two decimals.

A = 0.9177
z =
3.Medium
246259.25P = ?

The bag weights are normally distributed with mean 250 g and standard deviation 5 g. What fraction lies between 246 and 259.25 g? Give P as a decimal.

μ = 250σ = 5x1 = 246x2 = 259.25
P =
4.Medium
30.539.2P = ?

The delivery times are normally distributed with mean 32 min and standard deviation 6 min. What fraction lies between 30.5 and 39.2 min? Give P as a decimal.

μ = 32σ = 6x1 = 30.5x2 = 39.2
P =
5.Hard
μ = 100x = ?99%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Find the value x below which 99% of them lie (the 99th percentile).

μ = 100σ = 15P = 99%
x = points
6.Hard
557085100115130145pointstop 85%

The IQ scores are normally distributed with mean 100 points and standard deviation 15 points. Drag the cut-off so the shaded top 85% is to the right of it. Find the cut-off x.

μ = 100 pointsσ = 15 points85%
x = points

Answer key

  1. 1. P(X > x) = 0.8749
  2. 2. z = 1.39
  3. 3. P = 0.756
  4. 4. P = 0.4836
  5. 5. x = 134.9 points
  6. 6. x = 84.4 points

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